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Special Linear Case: Proportional
Situations2.14
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I need potatoes!• I need a whole lot of potatoes to make some delicious potato soup for a huge party
Yummy!
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Two Options
Costco:
- Pay $20 membership fee
- $2 per pound of potatoes
Lucky’s:
- $4 per pound of potatoes
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Let x = number of poundsLet y = total cost
Costco:
- Pay $20 membership fee
- $2 per pound of potatoes
•y = 2x + 20
Lucky’s:
- $4 per pound of potatoes
•y = 4xWhat’s different about the equation for Lucky’s?
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• Costco: y = 2x + 20 • Lucky’s: y = 4x
What’s different about the graph for Lucky’s?
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𝑦=23𝑥
𝑦=3 𝑥 𝑦=13𝑥
What’s true about all of these graphs?
What’s true about all of these equations?
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Notes•Proportional situations: x and y coordinates create equivalent fractions
•Can rewrite as a linear equation in slope-intercept form
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Vocabulary•Proportional linear equations = have an initial value (y-intercept, b) of 0
•Direct Variation = another name for a proportional relationship
• “y varies directly as x” means the graph is proportional
•Constant of Variation = the slope (m) of a proportional linear equation
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Team PracticeUsing any method your team comes up with, determine if the points in the table represent a proportional relationship or not.
x 2 3 4 10y 8 12 16 40
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Practice: Proportional or not?
x 3 4 5 6y 5 7 9 11
x 4 6 8 10y 6 9 12 15
x 12 15 18 24y 8 10 12 16